On seismic deghosting using Green’s theorem

Abstract

We have examined theoretically how receiver-side deghosting of pressure measurements can be derived from the Green’s theorem method. We split the Green’s function that obeys Dirichlet boundary conditions on the sea surface and at the receiver plane into two contributions: the first emitting energy downward only from its source location and the other emitting energy only upward. Using the normal derivative of the source-side downgoing Green’s function in the Green’s theorem evaluation over the receiver plane, the upgoing part of the pressure field is predicted. This is the receiver-side deghosted field. By inserting the source-side upgoing normal derivative Green’s function in Green’s theorem, its evaluation over the receiver plane predicts the downgoing part of the pressure field. For a plane horizontal receiver surface, the required Green’s function can be derived using the image series expansion method. To display the fundamental frequencies of this Green’s function, we have applied a Fourier series expansion of the Green’s function. Our theory gives a new understanding of and generalizes and simplifies previously published theories on Green’s theorem-based receiver-side deghosting of pressure wavefields.